This week in Pre-Calc 11, I learned how to convert irrational trinomials to perfect square trinomials and apply them to solve quadratic equations. However, before we can start solving quadratic equations with perfect square trinomials we must first understand how to recognize and complete them.

Let’s start with recognizing a perfect square trinomial. A sure fire way to to identify a perfect square trinomial is by looking at it’s first and third term. In a perfect square trinomial the first and third term are always a perfect square think of 4, 9, 16 25.. Ect, and half of the second term is the product of the the root of first and third multiplied.

Now, the second skill you need to learn to solve quadratic equations with perfect squares is completing square trinomials. You can do this by dividing the second term by two then squaring it  to find the missing term.

Now that you have learned the skills needed let’s apply what we learnt into converting an irrational trinomial and turn it into a perfect square trinomial in order to isolate X. In our example here we can clearly tell this equation as the third term is not a perfect square. So our first step is to find out what will complete our perfect square.

As we learned earlier we can find our missing term by dividing the second term by two then squaring it to find the missing term. So that’s exactly what we are gonna do here.

And now we know our missing term. We add the amount needed to get our third term to 9 and what we do on one side of the equation we must do on the other side.

Now we convert our perfect trinomial back into a perfect binomial.

We get rid of the square by square rooting both side.

Now we isolate X by subtracting 3 leaving us with our answer.